Finite Group Databasebeta

← C3×C5×#2325 #14275359

Subgroups — C3×C5×#2325 #14275359

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#121C211yesmaximal, characteristic
2C2×C3×C4×C5×D4C212yesmaximal, complemented
3C3×C5×#388C212yesmaximal, complemented
4C3×C5×#387C212yesmaximal, complemented
5C3×C5×#386C212yesmaximal, complemented
6C3×C5×#386C212yesmaximal, complemented
7C3×C5×#385C212yesmaximal, complemented
8C3×C5×#380C211yesmaximal, characteristic, complemented
9C2×C3×C5×#95C211yesmaximal, characteristic, complemented
10C5×#2325C311yesmaximal, characteristic, direct product factor, Hall
11C22×C3×C5×D4C2212yes—
12C22×C3×C5×D4C2211yescharacteristic
13C23×C3×C4×C5C2212yes—
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C3×C5×#121C418yescomplemented
18C3×C4×C5×D4—28no—
19C2×C3×C5×C4⋊C4C2212yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2212yes—
25C2×C3×C5×C22⋊C4C2212yes—
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C42×C5C2212yes—
29C3×C5×#95C2212yes—
30C3×C5×#95C2212yes—
31C3×C5×#95C2212yes—
32C3×C5×#95C2212yes—
33C3×C5×#95C2212yes—
34C3×#2325C511yesmaximal, characteristic, direct product factor, Hall
35C2×C5×#121C2×C311yescharacteristic
36C2×C4×C5×D4C2×C312yescomplemented
37C5×#388C2×C312yescomplemented
38C5×#387C2×C312yescomplemented
39C5×#386C2×C312yescomplemented
40C5×#386C2×C312yescomplemented
41C5×#385C2×C312yescomplemented
42C5×#380C2×C311yescharacteristic, complemented
43C2×C5×#95C2×C311yescharacteristic, complemented
44C24×C3×C5C2312yes—
45C24×C3×C5C2311yescharacteristic
46C2×C3×C5×D4—24no—
47C2×C3×C5×D4—24no—
48C2×C3×C5×D4—41no—
49C2×C3×C5×D4—41no—
50C2×C3×C5×D4C2×C418yescomplemented
51C2×C3×C5×D4C2×C414yescomplemented
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—24no—
54C22×C3×C4×C5—41no—
55C22×C3×C4×C5—41no—
56C22×C3×C4×C5—41no—
57C22×C3×C4×C5—41no—
58C22×C3×C4×C5—42no—
59C22×C3×C4×C5—42no—
60C22×C3×C4×C5—41no—
61C22×C3×C4×C5—41no—
62C22×C3×C4×C5C2×C414yescomplemented
63C22×C3×C4×C5D414yescomplemented
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2312yes—
71C3×C5×C4⋊C4—24no—
72C3×C5×C4⋊C4—41no—
73C3×C5×C4⋊C4—41no—
74C3×C5×C4⋊C4C2×C414yescomplemented
75C3×C5×C22⋊C4—24no—
76C3×C5×C22⋊C4—24no—
77C3×C5×C22⋊C4—42no—
78C3×C5×C22⋊C4—42no—
79C3×C5×C22⋊C4C2×C418yescomplemented
80C3×C42×C5—24no—
81C2×C3×#121C2×C511yescharacteristic
82C2×C3×C4×D4C2×C512yescomplemented
83C3×#388C2×C512yescomplemented
84C3×#387C2×C512yescomplemented
85C3×#386C2×C512yescomplemented
86C3×#386C2×C512yescomplemented
87C3×#385C2×C512yescomplemented
88C3×#380C2×C511yescharacteristic, complemented
89C2×C3×#95C2×C511yescharacteristic, complemented
90C22×C5×D4C22×C312yes—
91C22×C5×D4C22×C311yescharacteristic
92C23×C4×C5C22×C311yescharacteristic
93C23×C4×C5C22×C312yes—
94C23×C4×C5C22×C311yescharacteristic
95C23×C4×C5C22×C311yescharacteristic
96C5×#121C3×C418yescomplemented
97C4×C5×D4—28no—
98C2×C5×C4⋊C4C22×C312yes—
99C2×C5×C4⋊C4C22×C311yescharacteristic
100C2×C5×C4⋊C4C22×C311yescharacteristic
101C2×C5×C4⋊C4C22×C311yescharacteristic
102C2×C5×C22⋊C4C22×C312yes—
103C2×C5×C22⋊C4C22×C312yes—
104C2×C5×C22⋊C4C22×C312yes—
105C2×C5×C22⋊C4C22×C312yes—
106C2×C5×C22⋊C4C22×C312yes—
107C2×C42×C5C22×C312yes—
108C5×#95C22×C312yes—
109C5×#95C22×C312yes—
110C5×#95C22×C312yes—
111C5×#95C22×C312yes—
112C5×#95C22×C312yes—
113#2325C3×C511yescharacteristic, direct product factor, Sylow
114C23×C3×C5—21no—
115C23×C3×C5—21no—
116C23×C3×C5—21no—
117C23×C3×C5—21no—
118C23×C3×C5—22no—
119C23×C3×C5—22no—
120C23×C3×C5—22no—
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C414yes—
125C23×C3×C5C22×C412yes—
126C23×C3×C5C2×D412yes—
127C23×C3×C5#4112yes—
128C23×C3×C5C2411yescharacteristic
129C3×C5×D4—216no—
130C3×C5×D4—44no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—44no—
149C2×C3×C4×C5—44no—
150C2×C3×C4×C5—48no—
151C2×C3×C4×C5—44no—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C22×C414yes—
154C2×C3×C4×C5C22×C412yes—
155C2×C3×C4×C5C2×D414yes—
156C22×C3×D4C22×C512yes—
157C22×C3×D4C22×C511yescharacteristic
158C23×C3×C4C22×C511yescharacteristic
159C23×C3×C4C22×C512yes—
160C23×C3×C4C22×C511yescharacteristic
161C23×C3×C4C22×C511yescharacteristic
162C3×#121C4×C518yescomplemented
163C3×C4×D4—28no—
164C2×C3×C4⋊C4C22×C512yes—
165C2×C3×C4⋊C4C22×C511yescharacteristic
166C2×C3×C4⋊C4C22×C511yescharacteristic
167C2×C3×C4⋊C4C22×C511yescharacteristic
168C2×C3×C22⋊C4C22×C512yes—
169C2×C3×C22⋊C4C22×C512yes—
170C2×C3×C22⋊C4C22×C512yes—
171C2×C3×C22⋊C4C22×C512yes—
172C2×C3×C22⋊C4C22×C512yes—
173C2×C3×C42C22×C512yes—
174C3×#95C22×C512yes—
175C3×#95C22×C512yes—
176C3×#95C22×C512yes—
177C3×#95C22×C512yes—
178C3×#95C22×C512yes—
179C24×C5C23×C312yes—
180C24×C5C23×C311yescharacteristic
181C2×C5×D4—24no—
182C2×C5×D4—24no—
183C2×C5×D4—41no—
184C2×C5×D4—41no—
185C2×C5×D4C2×C3×C418yescomplemented
186C2×C5×D4C2×C3×C414yescomplemented
187C22×C4×C5—22no—
188C22×C4×C5—24no—
189C22×C4×C5—41no—
190C22×C4×C5—41no—
191C22×C4×C5—41no—
192C22×C4×C5—41no—
193C22×C4×C5—42no—
194C22×C4×C5—42no—
195C22×C4×C5—41no—
196C22×C4×C5—41no—
197C22×C4×C5C2×C3×C414yescomplemented
198C22×C4×C5C3×D414yescomplemented
199C22×C4×C5C23×C312yes—
200C22×C4×C5C23×C312yes—
201C22×C4×C5C23×C312yes—
202C22×C4×C5C23×C312yes—
203C22×C4×C5C23×C311yescharacteristic
204C22×C4×C5C23×C311yescharacteristic
205C22×C4×C5C23×C312yes—
206C5×C4⋊C4—24no—
207C5×C4⋊C4—41no—
208C5×C4⋊C4—41no—
209C5×C4⋊C4C2×C3×C414yescomplemented
210C5×C22⋊C4—24no—
211C5×C22⋊C4—24no—
212C5×C22⋊C4—42no—
213C5×C22⋊C4—42no—
214C5×C22⋊C4C2×C3×C418yescomplemented
215C42×C5—24no—
216C2×#121C2×C3×C511yescharacteristic
217C2×C4×D4C2×C3×C512yescomplemented
218#388C2×C3×C512yescomplemented
219#387C2×C3×C512yescomplemented
220#386C2×C3×C512yescomplemented
221#386C2×C3×C512yescomplemented
222#385C2×C3×C512yescomplemented
223#380C2×C3×C511yescharacteristic, complemented
224C2×#95C2×C3×C511yescharacteristic, complemented
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5—22no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—24no—
232C22×C3×C5—24no—
233C22×C3×C5—24no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5—42no—
238C22×C3×C5C4×D414yes—
239C22×C3×C5C23×C411yescharacteristic
240C22×C3×C5C22×D411yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5H(5,𝔽2)11yescharacteristic
243C22×C3×C5H(5,𝔽2)11yescharacteristic
244C22×C3×C5H(5,𝔽2)11yescharacteristic
245C22×C3×C52−1+411yescharacteristic
246C3×C4×C5—24no—
247C3×C4×C5—22no—
248C3×C4×C5—22no—
249C3×C4×C5—24no—
250C3×C4×C5—42no—
251C3×C4×C5—42no—
252C3×C4×C5—42no—
253C24×C3C23×C512yes—
254C24×C3C23×C511yescharacteristic
255C2×C3×D4—24no—
256C2×C3×D4—24no—
257C2×C3×D4—41no—
258C2×C3×D4—41no—
259C2×C3×D4C2×C4×C518yescomplemented
260C2×C3×D4C2×C4×C514yescomplemented
261C22×C3×C4—22no—
262C22×C3×C4—24no—
263C22×C3×C4—41no—
264C22×C3×C4—41no—
265C22×C3×C4—41no—
266C22×C3×C4—41no—
267C22×C3×C4—42no—
268C22×C3×C4—42no—
269C22×C3×C4—41no—
270C22×C3×C4—41no—
271C22×C3×C4C2×C4×C514yescomplemented
272C22×C3×C4C5×D414yescomplemented
273C22×C3×C4C23×C512yes—
274C22×C3×C4C23×C512yes—
275C22×C3×C4C23×C512yes—
276C22×C3×C4C23×C511yescharacteristic
277C22×C3×C4C23×C512yes—
278C22×C3×C4C23×C511yescharacteristic
279C22×C3×C4C23×C512yes—
280C3×C4⋊C4—24no—
281C3×C4⋊C4—41no—
282C3×C4⋊C4—41no—
283C3×C4⋊C4C2×C4×C514yescomplemented
284C3×C22⋊C4—24no—
285C3×C22⋊C4—24no—
286C3×C22⋊C4—42no—
287C3×C22⋊C4—42no—
288C3×C22⋊C4C2×C4×C518yescomplemented
289C3×C42—24no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—21no—
294C23×C5—22no—
295C23×C5—22no—
296C23×C5—22no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5C22×C3×C414yes—
301C23×C5C22×C3×C412yes—
302C23×C5C2×C3×D412yes—
303C23×C5C3×#4112yes—
304C23×C5C24×C311yescharacteristic
305C5×D4—216no—
306C5×D4—44no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—22no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—22no—
316C2×C4×C5—22no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—22no—
320C2×C4×C5—22no—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—44no—
325C2×C4×C5—44no—
326C2×C4×C5—48no—
327C2×C4×C5—44no—
328C2×C4×C5C22×C3×C412yes—
329C2×C4×C5C22×C3×C414yes—
330C2×C4×C5C22×C3×C412yes—
331C2×C4×C5C2×C3×D414yes—
332C22×D4C22×C3×C512yes—
333C22×D4C22×C3×C511yescharacteristic
334C23×C4C22×C3×C512yes—
335C23×C4C22×C3×C511yescharacteristic
336C23×C4C22×C3×C511yescharacteristic
337C23×C4C22×C3×C511yescharacteristic
338#121C3×C4×C518yescomplemented
339C4×D4—28no—
340C2×C4⋊C4C22×C3×C512yes—
341C2×C4⋊C4C22×C3×C511yescharacteristic
342C2×C4⋊C4C22×C3×C511yescharacteristic
343C2×C4⋊C4C22×C3×C511yescharacteristic
344C2×C22⋊C4C22×C3×C512yes—
345C2×C22⋊C4C22×C3×C512yes—
346C2×C22⋊C4C22×C3×C512yes—
347C2×C22⋊C4C22×C3×C512yes—
348C2×C22⋊C4C22×C3×C512yes—
349C2×C42C22×C3×C512yes—
350#95C22×C3×C512yes—
351#95C22×C3×C512yes—
352#95C22×C3×C512yes—
353#95C22×C3×C512yes—
354#95C22×C3×C512yes—
355C2×C3×C5—24no—
356C2×C3×C5—44no—
357C2×C3×C5C2×C4×D411yescharacteristic
358C2×C3×C5#51811yescharacteristic
359C2×C3×C5#52011yescharacteristic
360C2×C3×C5#53411yescharacteristic
361C2×C3×C5#53711yescharacteristic
362C2×C3×C5#53811yescharacteristic
363C2×C3×C5#53911yescharacteristic
364C23×C3—21no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3C22×C4×C514yes—
375C23×C3C22×C4×C512yes—
376C23×C3C2×C5×D412yes—
377C23×C3C5×#4112yes—
378C23×C3C24×C511yescharacteristic
379C3×D4—216no—
380C3×D4—44no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—44no—
399C2×C3×C4—44no—
400C2×C3×C4—48no—
401C2×C3×C4—44no—
402C2×C3×C4C22×C4×C512yes—
403C2×C3×C4C22×C4×C514yes—
404C2×C3×C4C22×C4×C512yes—
405C2×C3×C4C2×C5×D414yes—
406C22×C5—22no—
407C22×C5—22no—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—22no—
411C22×C5—22no—
412C22×C5—24no—
413C22×C5—24no—
414C22×C5—24no—
415C22×C5—42no—
416C22×C5—42no—
417C22×C5—42no—
418C22×C5—42no—
419C22×C5C3×C4×D414yes—
420C22×C5C23×C3×C411yescharacteristic
421C22×C5C22×C3×D411yescharacteristic
422C22×C5C2×C3×#4111yescharacteristic
423C22×C5C3×H(5,𝔽2)11yescharacteristic
424C22×C5C3×H(5,𝔽2)11yescharacteristic
425C22×C5C3×H(5,𝔽2)11yescharacteristic
426C22×C5C3×2−1+411yescharacteristic
427C4×C5—24no—
428C4×C5—22no—
429C4×C5—22no—
430C4×C5—24no—
431C4×C5—42no—
432C4×C5—42no—
433C4×C5—42no—
434C24C23×C3×C512yes—
435C24C23×C3×C511yescharacteristic
436C2×D4—24no—
437C2×D4—24no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C2×C3×C4×C518yescomplemented
441C2×D4C2×C3×C4×C514yescomplemented
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C2×C3×C4×C514yescomplemented
453C22×C4C3×C5×D414yescomplemented
454C22×C4C23×C3×C512yes—
455C22×C4C23×C3×C512yes—
456C22×C4C23×C3×C512yes—
457C22×C4C23×C3×C511yescharacteristic
458C22×C4C23×C3×C512yes—
459C22×C4C23×C3×C511yescharacteristic
460C22×C4C23×C3×C512yes—
461C4⋊C4—24no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×C3×C4×C514yescomplemented
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—42no—
468C22⋊C4—42no—
469C22⋊C4C2×C3×C4×C518yescomplemented
470C42—24no—
471C3×C5#232511yescharacteristic, direct product factor, Hall
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—42no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3C4×C5×D414yes—
486C22×C3C23×C4×C511yescharacteristic
487C22×C3C22×C5×D411yescharacteristic
488C22×C3C2×C5×#4111yescharacteristic
489C22×C3C5×H(5,𝔽2)11yescharacteristic
490C22×C3C5×H(5,𝔽2)11yescharacteristic
491C22×C3C5×H(5,𝔽2)11yescharacteristic
492C22×C3C5×2−1+411yescharacteristic
493C3×C4—24no—
494C3×C4—22no—
495C3×C4—22no—
496C3×C4—24no—
497C3×C4—42no—
498C3×C4—42no—
499C3×C4—42no—
500C2×C5—24no—
501C2×C5—44no—
502C2×C5C2×C3×C4×D411yescharacteristic
503C2×C5C3×#51811yescharacteristic
504C2×C5C3×#52011yescharacteristic
505C2×C5C3×#53411yescharacteristic
506C2×C5C3×#53711yescharacteristic
507C2×C5C3×#53811yescharacteristic
508C2×C5C3×#53911yescharacteristic
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23C22×C3×C4×C514yes—
520C23C22×C3×C4×C512yes—
521C23C2×C3×C5×D412yes—
522C23C3×C5×#4112yes—
523C23C24×C3×C511yescharacteristic
524D4—216no—
525D4—44no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—44no—
544C2×C4—44no—
545C2×C4—48no—
546C2×C4—44no—
547C2×C4C22×C3×C4×C512yes—
548C2×C4C22×C3×C4×C514yes—
549C2×C4C22×C3×C4×C512yes—
550C2×C4C2×C3×C5×D414yes—
551C2×C3—24no—
552C2×C3—44no—
553C2×C3C2×C4×C5×D411yescharacteristic
554C2×C3C5×#51811yescharacteristic
555C2×C3C5×#52011yescharacteristic
556C2×C3C5×#53411yescharacteristic
557C2×C3C5×#53711yescharacteristic
558C2×C3C5×#53811yescharacteristic
559C2×C3C5×#53911yescharacteristic
560C5C3×#232511yescharacteristic, direct product factor, Sylow
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—22no—
567C22—24no—
568C22—24no—
569C22—24no—
570C22—42no—
571C22—42no—
572C22—42no—
573C22—42no—
574C22C3×C4×C5×D414yes—
575C22C23×C3×C4×C511yescharacteristic
576C22C22×C3×C5×D411yescharacteristic
577C22C2×C3×C5×#4111yescharacteristic
578C22C3×C5×H(5,𝔽2)11yescharacteristic
579C22C3×C5×H(5,𝔽2)11yescharacteristic
580C22C3×C5×H(5,𝔽2)11yescharacteristic
581C22C3×C5×2−1+411yescharacteristic
582C4—24no—
583C4—22no—
584C4—22no—
585C4—24no—
586C4—42no—
587C4—42no—
588C4—42no—
589C3C5×#232511yescharacteristic, direct product factor, Sylow
590C2—24no—
591C2—44no—
592C2C2×C3×C4×C5×D411yescharacteristic
593C2C3×C5×#51811yescharacteristic
594C2C3×C5×#52011yescharacteristic
595C2C3×C5×#53411yescharacteristic
596C2C3×C5×#53711yescharacteristic
597C2C3×C5×#53811yescharacteristic
598C2C3×C5×#53911yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutatorC22C23×C3×C4×C5
Frattini, cosocleC23C24×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C3×C4×C5×D4C2semidirect
3. C3×C5×#388C2semidirect
4. C3×C5×#387C2semidirect
5. C3×C5×#386C2semidirect
6. C3×C5×#386C2semidirect
7. C3×C5×#385C2semidirect
8. C3×C5×#380C2semidirect
9. C2×C3×C5×#95C2semidirect
10. C5×#2325C3direct (N × H)
17. C3×C5×#121C4semidirect
34. C3×#2325C5direct (N × H)
36. C2×C4×C5×D4C2×C3semidirect
37. C5×#388C2×C3semidirect
38. C5×#387C2×C3semidirect
39. C5×#386C2×C3semidirect
40. C5×#386C2×C3semidirect
41. C5×#385C2×C3semidirect
42. C5×#380C2×C3semidirect
43. C2×C5×#95C2×C3semidirect
50. C2×C3×C5×D4C2×C4semidirect
51. C2×C3×C5×D4C2×C4semidirect
62. C22×C3×C4×C5C2×C4semidirect
63. C22×C3×C4×C5D4semidirect
74. C3×C5×C4⋊C4C2×C4semidirect
79. C3×C5×C22⋊C4C2×C4semidirect
82. C2×C3×C4×D4C2×C5semidirect
83. C3×#388C2×C5semidirect
84. C3×#387C2×C5semidirect
85. C3×#386C2×C5semidirect
86. C3×#386C2×C5semidirect
87. C3×#385C2×C5semidirect
88. C3×#380C2×C5semidirect
89. C2×C3×#95C2×C5semidirect
96. C5×#121C3×C4semidirect
113. #2325C3×C5direct (N × H)
162. C3×#121C4×C5semidirect
185. C2×C5×D4C2×C3×C4semidirect
186. C2×C5×D4C2×C3×C4semidirect
197. C22×C4×C5C2×C3×C4semidirect
198. C22×C4×C5C3×D4semidirect
209. C5×C4⋊C4C2×C3×C4semidirect
214. C5×C22⋊C4C2×C3×C4semidirect
217. C2×C4×D4C2×C3×C5semidirect
218. #388C2×C3×C5semidirect
219. #387C2×C3×C5semidirect
220. #386C2×C3×C5semidirect
221. #386C2×C3×C5semidirect
222. #385C2×C3×C5semidirect
223. #380C2×C3×C5semidirect
224. C2×#95C2×C3×C5semidirect
259. C2×C3×D4C2×C4×C5semidirect
260. C2×C3×D4C2×C4×C5semidirect
271. C22×C3×C4C2×C4×C5semidirect
272. C22×C3×C4C5×D4semidirect
283. C3×C4⋊C4C2×C4×C5semidirect
288. C3×C22⋊C4C2×C4×C5semidirect
338. #121C3×C4×C5semidirect
440. C2×D4C2×C3×C4×C5semidirect
441. C2×D4C2×C3×C4×C5semidirect
452. C22×C4C2×C3×C4×C5semidirect
453. C22×C4C3×C5×D4semidirect
464. C4⋊C4C2×C3×C4×C5semidirect
469. C22⋊C4C2×C3×C4×C5semidirect
471. C3×C5#2325direct (N × H)
560. C5C3×#2325direct (N × H)
589. C3C5×#2325direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×C5×#1212
C2×C3×C4×C5×D42
C3×C5×#3882
C3×C5×#3872
C3×C5×#3862
C3×C5×#3852
C3×C5×#3802
C2×C3×C5×#952
C5×#23253
C3×#23255